Air carrier FO reported the tow bar was not attached to the aircraft properly and disconnected causing the aircraft to contact the push tug.

Narrative

After the initial pushback and tug was released. We had both engine running and we were running after start checklist". I noticed that rampers were trying to get a hold of us and giving us stop sign with hand signal. I advised Captain what was going on and we stopped our process for taxi. Ground operation personnel hooked up the headset to the airplane and communicated to us that they forgot to offload inbound flight's bags; so we had to return to gate. We were also told that they will hook up the tug and they were going to tug us back to our original gate. Captain communicated with Ramper and he advised us to shut down engines and release the brake for tug hook up. Captain read back instruction and released the brake as instructed by him and Captain simultaneously told me to shut down the engines. As I shut down the engine; Ramper communicated us again and advised us to set brake again. Captain immediately pressed on brake. According to the operation personnel; airplane was not hooked up to tug properly; which led to undesirable movement of airplane. This caused the airplane to come in undesired contact with tug; which required inspection by the maintenance personnel to ensure no damage was done. Upon visual inspection; Maintenance cleared us from any damage. Subsequently; we were hooked up to the tug and they moved us back to original gate in order to offload the bags. Upon completion of offload; we proceeded to our flight."